After joining Zagreb mid-way through the 2009–10 season, and spending much of the 2010–11 season on loan with Dubrava, Šarić won the Città di Roma EuroLeague (IJT) in May 2011, alongside teammates, Mario Hezonja and Dominik Mavra, and progressed to the Final Four of the tournament, where his team eventually won.

[1] After he had registered a triple-double in the final game with 19 points, 14 rebounds and 10 assists, in addition to 10 drawn fouls, he was named the MVP of the tournament.

However, due to a sanction by FIBA, forcing the Spanish team to pay a buyout of €550,000, he didn't sign with Bilbao.

[14] Finally, Šarić withdrew from the draft altogether, because of his desire to stay in Europe for another year, to gain experience.

[5] In April 2014, he was selected into the ideal team and also named the MVP of the Adriatic League, averaging 16.7 points, 9.7 rebounds and 3.2 assists in the regular season.

[28] At the beginning of the 2014–15 season, Šarić's father criticized Efes's head coach, Dušan Ivković, for not putting Dario in the roster for the Turkish Super League games, openly threatening possible termination of the player's contract, if the situation didn't improve.

[49] Šarić was named a Rising Star once again during All-Star Weekend 2018, competing for the World team alongside 76ers teammates Joel Embiid and Ben Simmons.

[52] On 12 November 2018, Šarić was traded to the Minnesota Timberwolves, along with Jerryd Bayless, Robert Covington and a 2022 second-round pick, in exchange for Jimmy Butler and Justin Patton.

[59] He later matched his career-high of 17 rebounds, scoring 19 points this time around, in a 121–119 overtime loss to the San Antonio Spurs on 14 December in Mexico City.

[60] After losing his starting spot to Cameron Johnson in the 2020 NBA Bubble during the scrimmage games, Šarić returned as a starter on 10 August, getting 16 points and 9 rebounds in a blowout 128–101 win over the Oklahoma City Thunder.

Due to the success he had both as a starter last season and as a sixth man off the bench in the 2020 bubble setting, Šarić signed a three-year extension with the Suns on 28 November 2020.

[63] While he officially missed only four games to the virus, Šarić remained inactive for a month with leg injuries also affecting him for at least the first half of the season.

[65] On 2 March, Šarić lead the Suns in scoring with a season-high 21 points off the bench in a 114–104 win over the defending champion Los Angeles Lakers.

On February 9, 2023, Šarić was traded, alongside a 2029 second-round pick and cash considerations, to the Oklahoma City Thunder in exchange for Darius Bazley.

[69] Šarić made his Thunder debut on February 15, recording 12 points and five rebounds in a 133–96 win over the Houston Rockets.

[72] While playing with Croatia's Under-16 national team, Šarić was named the Most Valuable Player of the 2010 FIBA Europe Under-16 Championship in a unanimous vote, after leading the tournament in scoring (24.3 ppg) and rebounding (11.5 rpg), and finishing second in assists (5.8 apg).

[74] He won a gold medal with Croatia's Under-18 national team in the 2012 FIBA Europe Under-18 Championship, where he finished first in scoring (25.6 ppg) and second in rebounds (10.1 rpg).

[75] Soon after scoring 39 points to lead Croatia to victory in the gold medal game against Lithuania, Šarić was voted unanimously as tournament MVP.

[76] Šarić also played with Croatia's Under-19 national team in the 2011 FIBA Under-19 World Cup, where he finished fourth in scoring (18.1 ppg)[77] and third in rebounds (10.1 rpg),[78] despite being one of the youngest participants at 17 years of age.

He also played at the 2013 FIBA Under-19 World Cup, where he averaged 20.3 points, 11.2 rebounds, 4.9 assists per game, and was named to the All-Tournament Team.

[80] He then played with Croatia's senior men's team at the 2014 FIBA World Cup, where he averaged 11.7 points, 6.7 rebounds, and 2.3 assists per game.